Graph Snapshots Research Articles

Dynamic graph convolutional networks with attention mechanism for rumor detection on social media

Social media has become an ideal platform for the propagation of rumors, fake news, and misinformation. Rumors on social media not only mislead online users but also affect the real world immensely. Thus, detecting the rumors and preventing their spread became an essential task. Some of the recent deep learning-based rumor detection methods, such as Bi-Directional Graph Convolutional Networks (Bi-GCN), represent rumor using the completed stage of the rumor diffusion and try to learn the structural information from it. However, these methods are limited to represent rumor propagation as a static graph, which isn’t optimal for capturing the dynamic information of the rumors. In this study, we propose novel graph convolutional networks with attention mechanisms, named Dynamic GCN, for rumor detection. We first represent rumor posts with their responsive posts as dynamic graphs. The temporal information is used to generate a sequence of graph snapshots. The representation learning on graph snapshots with attention mechanism captures both structural and temporal information of rumor spreads. The conducted experiments on three real-world datasets demonstrate the superiority of Dynamic GCN over the state-of-the-art methods in the rumor detection task.

On querying historical k-cores

Many real-world relationships between entities can be modeled as temporal graphs, where each edge is associated with a timestamp or a time interval representing its occurrence. K -core is a fundamental model used to capture cohesive subgraphs in a simple graph and have drawn much research attention over the last decade. Despite widespread research, none of the existing works support the efficient querying of historical k -cores in temporal graphs. In this paper, given an integer k and a time window, we study the problem of computing all k -cores in the graph snapshot over the time window. We propose an index-based solution and several pruning strategies to reduce the index size. We also design a novel algorithm to construct this index, whose running time is linear to the final index size. Lastly, we conducted extensive experiments on several real-world temporal graphs to show the high effectiveness of our index-based solution.

Modeling Co-evolution of Attributed and Structural Information in Graph Sequence

Most graph neural network models learn embeddings of nodes in static attributed graphs for predictive analysis. Recent attempts have been made to learn temporal proximity of the nodes. We find that real dynamic attributed graphs exhibit complex phenomenon of co-evolution between node attributes and graph structure. Learning node embeddings for forecasting change of node attributes and evolution of graph structure over time remains an open problem. In this work, we present a novel framework called CoEvoGNN for modeling dynamic attributed graph sequence. It preserves the impact of earlier graphs on the current graph by embedding generation through the sequence of attributed graphs. It has a temporal self-attention architecture to model long-range dependencies in the evolution. Moreover, CoEvoGNN optimizes model parameters jointly on two dynamic tasks, attribute inference and link prediction over time. So the model can capture the co-evolutionary patterns of attribute change and link formation. This framework can adapt to any graph neural algorithms so we implemented and investigated three methods based on it: CoEvoGCN, CoEvoGAT, and CoEvoSAGE. Experiments demonstrate the framework (and its methods) outperforms strong baseline methods on predicting an entire unseen graph snapshot of personal attributes and interpersonal links in dynamic social graphs and financial graphs.

Raphtory: Streaming analysis of distributed temporal graphs

Temporal graphs capture the development of relationships within data throughout time. This model fits naturally within a streaming architecture, where new events can be inserted directly into the graph upon arrival from a data source and be compared to related entities or historical state. However, the vast majority of graph processing systems only consider traditional graph analysis on static data, with some outliers supporting batched updating and temporal analysis across graph snapshots. In this work we define a temporal graph model which can be updated via event streams and discuss the challenges of distribution and graph maintenance. To solve these challenges, we introduce Raphtory, a distributed temporal graph management system which maintains the full graph history in memory, leveraging this to insert streamed events directly into the model without batching or centralised ordering. Raphtory additionally provides an API to perform both approximative analysis on the most up-to-date version of the graph, as well as temporal analysis throughout its full history; executed in parallel with ingestion.

Node embeddings in dynamic graphs

In this paper, we present algorithms that learn and update temporal node embeddings on the fly for tracking and measuring node similarity over time in graph streams. Recently, several representation learning methods have been proposed that are capable of embedding nodes in a vector space in a way that captures the network structure. Most of the known techniques extract embeddings from static graph snapshots. By contrast, modeling the dynamics of the nodes in temporal networks requires evolving node representations. In order to update node representations that reflect the temporal changes in the local graph structure, we rely on ideas for data stream algorithms. For example, we assess neighborhood overlap by a MinHash fingerprint-based algorithm.To evaluate our methods, in addition to the standard link prediction task, we provide dynamic ground truth data for the quantitative evaluation of similarity search by using online updated node embeddings. In our experiments, we constructed tennis tournament Twitter mention graphs as edge streams and compiled dynamic ground truth by using tournament schedule as external source. Our new algorithms outperformed snapshot-based batch methods for both link prediction and similarity search.

STVG: an evolutionary graph framework for analyzing fast-evolving networks

Sequence of graph snapshots have been commonly utilized in literature to represent changes in a dynamic graph. This approach may be suitable for small-size and slowly evolving graphs; however, it is associated with high storage overhead in massive and fast-evolving graphs because of replication of the entire graph from one snapshot to another at shorter temporal resolutions. This presents a drawback especially where efficient evolutionary analytics relies on the explanatory power of representing the dynamics of the graph across different temporal resolutions. In this paper, we propose a framework based on our Space–Time-varying graph (STVG) formalism which utilizes the Whole-graph approach to model the dynamics of a graph such that the evolution of the graph materializes in the time-varying changes of its Projected graphs. The STVG framework provides an approach to reduce high storage overhead in massively changing graph where new nodes and edges arrive every second. It affords the capability to extract Projected graphs at different time-windows and analyze their metrics across varying temporal resolutions. We demonstrate how the proposed STVG framework can be exploited to identify and extract evolutionary patterns in public bus transit graph using metrics such as graph density, volume and average path length. The results reveal evolutionary patterns in the overall network density, traffic congestion density as well as graph density with respect to bus movement at hourly, daily and monthly temporal resolutions.

Top- Durable Graph Pattern Queries on Temporal Graphs

Graphs offer a natural model for the relationships and interactions among entities, such as those occurring among users in social and cooperation networks, and proteins in biological networks. Since most such networks are dynamic, to capture their evolution over time, we assume a sequence of graph snapshots where each graph snapshot represents the state of the network at a different time instance. Given this sequence, we seek to find the top- $k$ most durable matches of an input graph pattern query, that is, the matches that exist for the longest period of time. The straightforward way to address this problem is to apply a state-of-the-art graph pattern matching algorithm at each snapshot and then aggregate the results. However, for large networks and long sequences, this approach is computationally expensive, since all matches have to be generated at each snapshot, including those appearing only once. We propose a new approach that uses a compact representation of the sequence of graph snapshots, appropriate time indexes to prune the search space, and strategies to determine the duration of the seeking matches. Finally, we present experiments with real datasets that illustrate the efficiency and effectiveness of our approach.

Finding lasting dense subgraphs

Graphs form a natural model for relationships and interactions between entities, for example, between people in social and cooperation networks, servers in computer networks, or tags and words in documents and tweets. But, which of these relationships or interactions are the most lasting ones? In this paper, we study the following problem: given a set of graph snapshots, which may correspond to the state of an evolving graph at different time instances, identify the set of nodes that are the most densely connected in all snapshots. We call this problem the Best Friends For Ever (BFF) problem. We provide definitions for density over multiple graph snapshots, that capture different semantics of connectedness over time, and we study the corresponding variants of the BFF problem. We then look at the On-Off BFF (O^2BFF) problem that relaxes the requirement of nodes being connected in all snapshots, and asks for the densest set of nodes in at least $k$ of a given set of graph snapshots. We show that this problem is NP-complete for all definitions of density, and we propose a set of efficient algorithms. Finally, we present experiments with synthetic and real datasets that show both the efficiency of our algorithms and the usefulness of the BFF and the O^2BFF problems.

Temporal walk based centrality metric for graph streams

A plethora of centrality measures or rankings have been proposed to account for the importance of the nodes of a network. In the seminal study of Boldi and Vigna (2014), the comparative evaluation of centrality measures was termed a difficult, arduous task. In networks with fast dynamics, such as the Twitter mention or retweet graphs, predicting emerging centrality is even more challenging.Our main result is a new, temporal walk based dynamic centrality measure that models temporal information propagation by considering the order of edge creation. Dynamic centrality measures have already started to emerge in publications; however, their empirical evaluation is limited. One of our main contributions is creating a quantitative experiment to assess temporal centrality metrics. In this experiment, our new measure outperforms graph snapshot based static and other recently proposed dynamic centrality measures in assigning the highest time-aware centrality to the actually relevant nodes of the network. Additional experiments over different data sets show that our method perform well for detecting concept drift in the process that generates the graphs.

Dynamic graphs, community detection, and Riemannian geometry

A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time – dynamic community detection – and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and find that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include producing a Riemannian least-squares regression method for working with noisy data and developing support methods, such as spectral sparsification, to improve the scalability of our current methods.

Promising Ideas for Collective Advancement of Communal Knowledge Using Temporal Analytics and Cluster Analysis

Understanding ideas in a discourse is challenging, especially in textual discourse analysis. We propose using temporal analytics with unsupervised machine learning techniques to investigate promising ideas for the collective advancement of communal knowledge in an online knowledge building discourse. A discourse unit network was constructed and temporal analysis was carried out to identify promising ideas, which are improvable perceptions of significant relevance that aid in the understanding of discourse context and content. With the aid of a degree centrality–betweenness centrality (DC-BC) graph, more promising ideas were discovered. An additional analysis using multiple DC-BC graph snapshots at different discourse junctures illustrates the transition of these promising ideas over time. Machine learning in the form of k-means clustering further categorized promising ideas. Cluster centroids were calculated and represented the foci of discussions, while the movement of discourse units about cluster centroids reflected how ideas affected learning behaviours among the participants. Discourse units containing promising ideas were qualitatively verified. Overall, the results showed that the implementation of temporal analytics and clustering provided insights and feedback to users about idea-related processes in the discourse. The findings have implications for teachers, students, and researchers

Clone temporal centrality measures for incomplete sequences of graph snapshots

BackgroundDifferent phenomena like the spread of a disease, social interactions or the biological relation between genes can be thought of as dynamic networks. These can be represented as a sequence of static graphs (so called graph snapshots). Based on this graph sequences, classical vertex centrality measures like closeness and betweenness centrality have been extended to quantify the importance of single vertices within a dynamic network. An implicit assumption for the calculation of temporal centrality measures is that the graph sequence contains all information about the network dynamics over time. This assumption is unlikely to be justified in many real world applications due to limited access to fully observed network data. Incompletely observed graph sequences lack important information about duration or existence of edges and may result in biased temporal centrality values.ResultsTo account for this incompleteness, we introduce the idea of extending original temporal centrality metrics by cloning graphs of an incomplete graph sequence. Focusing on temporal betweenness centrality as an example, we show for different simulated scenarios of incomplete graph sequences that our approach improves the accuracy of detecting important vertices in dynamic networks compared to the original methods. An age-related gene expression data set from the human brain illustrates the new measures. Additional results for the temporal closeness centrality based on cloned snapshots support our findings. We further introduce a new algorithm called REN to calculate temporal centrality measures. Its computational effort is linear in the number of snapshots and benefits from sparse or very dense dynamic networks.ConclusionsWe suggest to use clone temporal centrality measures in incomplete graph sequences settings. Compared to approaches that do not compensate for incompleteness our approach will improve the detection rate of important vertices. The proposed REN algorithm allows to calculate (clone) temporal centrality measures even for long snapshot sequences.

Processing Concurrent Graph Analytics with Decoupled Computation Model

Graph processing systems have been widely used in enterprises like online social networks to process their daily jobs. With the fast growing of social applications, they have to efficiently handle massive concurrent jobs. However, due to the inherent design for a single job, existing systems incur great inefficiency in terms of memory usage, execution and fault tolerance. Motivated by this issue, in this paper we introduce Seraph, a graph processing system that enables efficient job-level parallelism. Seraph is designed based on a decoupled computation model, which decouples both the runtime job data and the computation logic. Decoupling the runtime data allows multiple concurrent jobs to share graph structure data in memory, which fundamentally increases job-level concurrency and reduces fault tolerance overhead. Decoupling computation logic could extend scheduling space, which benefits both execution performance and memory consumption. Seraph adopts a copy-on-write semantic to isolate the graph mutation of concurrent jobs, and a lazy snapshot protocol to generate consistent graph snapshots for jobs submitted at different time. Based on the decoupled model, it provides unified programming interfaces for both synchronous and asynchronous graph applications. Moreover, Seraph implements a lightweight checkpoint mechanism which can tremendously reduce the fault tolerance overhead. The evaluation results show that Seraph significantly outperforms popular systems (such as Giraph, Spark, GraphX and PowerLyra) in both memory usage and job completion time, when executing concurrent graph jobs.

Automatic algorithm transformation for efficient multi-snapshot analytics on temporal graphs

Analytical graph algorithms commonly compute metrics for a graph at one point in time. In practice it is often also of interest how metrics change over time, e.g., to find trends. For this purpose, algorithms must be executed for multiple graph snapshots. We present Single Algorithm Multiple Snapshots (SAMS) , a novel approach to execute algorithms concurrently for multiple graph snapshots. SAMS automatically transforms graph algorithms to leverage similarities between the analyzed graph snapshots. The automatic transformation interleaves algorithm executions on multiple snapshots, synergistically shares their graph accesses and traversals, and optimizes the algorithm's data layout. Thus, SAMS can amortize the cost of random data accesses and improve memory bandwidth utilization---two main cost factors in graph analytics. We extensively evaluate SAMS using six well-known algorithms and multiple synthetic as well as real-world graph datasets. Our measurements show that in multi-snapshot analyses, SAMS offers runtime improvements of up to two orders of magnitude over traditional snapshot-at-a-time execution.

Scalable Temporal Latent Space Inference for Link Prediction in Dynamic Social Networks

We propose a temporal latent space model for link prediction in dynamic social networks, where the goal is to predict links over time based on a sequence of previous graph snapshots. The model assumes that each user lies in an unobserved latent space, and interactions are more likely to occur between similar users in the latent space representation. In addition, the model allows each user to gradually move its position in the latent space as the network structure evolves over time. We present a global optimization algorithm to effectively infer the temporal latent space. Two alternative optimization algorithms with local and incremental updates are also proposed, allowing the model to scale to larger networks without compromising prediction accuracy. Empirically, we demonstrate that our model, when evaluated on a number of real-world dynamic networks, significantly outperforms existing approaches for temporal link prediction in terms of both scalability and predictive power.

Toward continuous pattern detection over evolving large graph with snapshot isolation

This paper studies continuous pattern detection over large evolving graphs, which plays an important role in monitoring-related applications. The problem is challenging due to the large size and dynamic updates of graphs, the massive search space of pattern detection and inconsistent query results on dynamic graphs. This paper first introduces a snapshot isolation requirement, which ensures that the query results come from a consistent graph snapshot instead of a mixture of partial evolving graphs. Second, we propose an SSD (single sink directed acyclic graph) plan friendly to vertex-centric-distributed graph processing frameworks. SSD plan can guide the message transformation and transfer among graph vertices, and determine the satisfaction of the pattern on graph vertices for the sink vertex. Third, we devise strategies for major steps in the SSD evaluation, including the location of valid messages to achieve snapshot isolation, AO-List to determine the satisfaction of transition rule over dynamic graph, and message-on-change policy to reduce outgoing messages. The experiments on billion-edge graphs using Giraph, an open source implementation of Pregel, illustrate the efficiency and effectiveness of our method.

A regularized graph layout framework for dynamic network visualization

Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual representation of the network structure at each time step, the sequence should preserve the mental map between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network. In this paper, we propose a framework for dynamic network visualization in the on-line setting where only present and past graph snapshots are available to create the present layout. The proposed framework creates regularized graph layouts by augmenting the cost function of a static graph layout algorithm with a grouping penalty, which discourages nodes from deviating too far from other nodes belonging to the same group, and a temporal penalty, which discourages large node movements between consecutive time steps. The penalties increase the stability of the layout sequence, thus preserving the mental map. We introduce two dynamic layout algorithms within the proposed framework, namely dynamic multidimensional scaling and dynamic graph Laplacian layout. We apply these algorithms on several data sets to illustrate the importance of both grouping and temporal regularization for producing interpretable visualizations of dynamic networks.

Intrinsically dynamic network communities

Community finding algorithms for networks have recently been extended to dynamic data. Most of these recent methods aim at exhibiting community partitions from successive graph snapshots and thereafter connecting or smoothing these partitions using clever time-dependent features and sampling techniques. These approaches are nonetheless achieving longitudinal rather than dynamic community detection. We assume that communities are fundamentally defined by the repetition of interactions among a set of nodes over time. According to this definition, analyzing the data by considering successive snapshots induces a significant loss of information: we suggest that it blurs essentially dynamic phenomena—such as communities based on repeated inter-temporal interactions, nodes switching from a community to another across time, or the possibility that a community survives while its members are being integrally replaced over a longer time period. We propose a formalism which aims at tackling this issue in the context of time-directed datasets (such as citation networks), and present several illustrations of both empirical and synthetic dynamic networks. We eventually introduce intrinsically dynamic metrics to qualify temporal community structure and emphasize their possible role as an estimator of the quality of the community detection—taking into account the fact that various empirical contexts may call for distinct ‘community’ definitions and detection criteria.

An event-based framework for characterizing the evolutionary behavior of interaction graphs

Interaction graphs are ubiquitous in many fields such as bioinformatics, sociology and physical sciences. There have been many studies in the literature targeted at studying and mining these graphs. However, almost all of them have studied these graphs from a static point of view. The study of the evolution of these graphs over time can provide tremendous insight on the behavior of entities, communities and the flow of information among them. In this work, we present an event-based characterization of critical behavioral patterns for temporally varying interaction graphs. We use nonoverlapping snapshots of interaction graphs and develop a framework for capturing and identifying interesting events from them. We use these events to characterize complex behavioral patterns of individuals and communities over time. We show how semantic information can be incorporated to reason about community-behavior events. We also demonstrate the application of behavioral patterns for the purposes of modeling evolution, link prediction and influence maximization. Finally, we present a diffusion model for evolving networks, based on our framework.